Original title: Full-Model Optimality for Tunable Linear Generative Priors in Compressed Sensing
Zhaoming Li, Paul Hand · September 2026
When scientists reconstruct images or signals from incomplete measurements, they use compressed sensing. To fill in the missing information, they rely on priors, which are models of what the original data should look like. Past experiments showed that tuning a model's complexity at reconstruction time could lower errors. In this paper, researchers analyzed a theoretical setup with a family of linear priors connected by singular value decompositions. These linear models describe data using simple straight-line mathematical relationships. The authors tested how these priors perform during noiseless Gaussian compressed sensing. They proved that the full-dimensional linear prior always gets the lowest expected reconstruction error across the entire family. Dialing down to a simpler prior does not help here. This means past experimental benefits from tuning must come from nonlinearities in neural network models.
Imagine you are following a recipe to bake a cake. A recipe with exact measurements for every ingredient might seem overly detailed, but it ensures the cake turns out perfectly every time. If you simplify by guessing measurements to save time, the cake could sink or taste off. In this paper, for this specific type of problem, the most detailed set of instructions—like the full recipe—leads to the best outcome, just as precise measurements prevent baking errors.
This affects engineers and scientists using AI to rebuild signals from limited data. It shows that in ideal cases, sticking with the most detailed model is best, which guides how we design these systems in practice.
The paper only considers a noiseless and linear setting. It does not address what happens with noise, nonlinear models, or real-world data that does not follow Gaussian distributions. The result is specific to this idealized case and may not apply to practical scenarios.
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Full-Model Optimality for Tunable Linear Generative Priors in Compressed Sensing — Zhaoming Li, Paul Hand
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.